Question Hi. Take the following syllogism : John believes that green people should be killed. Mushmush is a green person, a neighbour of John. ====================== Thus, John believes that Mushmush should be killed. Formally, the argument seems valid. However, in reality it doesn't work. A persona can believe that all people with quality X should be killed, but not think it about a specific person he knows. So is there a logical contradiction here? What happens? Thank you, Sam

Accepted:
December 24, 2009

Comments

The syllogism is still valid (i.e., if the two premises were true, the conclusion would have to be true). But you have just found a case (Mushmush) that falsifies the first premise. It turns out John does not really believe that all green people should be killed, but he believes (at least) one green person (Mushmush) should not be killed. Good for logic and good for Mushmush!

Whoa! With all due respect to Professor Nahmias, he is mistaken. The syllogism is NOT valid and here is why. Propositions that are "in the scope" of words like belief can't be manipulated while preserving validity. So while,

Green people should be killed.

Mushmush is a green person.

ergo, Mushmush should be killed

is valid, embedding the first premise in the scope of belief ('John believes that green people should be killed') will destroy the argument's validity. Words like 'believes' (and related ones such as 'knows', 'wants', 'fears') create what is known as opaque contexts, in which inferences that would otherwise be valid are no longer valid. The reason is that what a person believes (knows, wants, fears) depends not only on what is implied by the propositions he believes, but also on whether he *realizes* that these things are implied. Alas, we are all too often unaware of what is implied by the things that we believe.

The point here has been discussed in detail by philosophers like Quine ('Quantifiers and propositional attitudes'), and Kaplan ('Quantifying in') and gets a thorough treatment in more recent textbook discussions such as Cherchia and McConnell-Ginet's _Meaning and Grammar_.

Mitch Green

With all due respect to Professor Green (hi, Mitch!), even that is not the final word. I think perhaps Professor Nahmias was assuming that John knows perfectly well that Mushmush is a green person, Mushmush being his neighbor and all that, and that John has some minimal degree of logical competence.

Still in that case, most people would hold that it does not logically follow that John believes that Mushmush should be killed. There are two quite different reasons for this.

One involves the fact that we cannot, even in principle, actually deduce all the logical consequences of everything we believe. It seems extremely plausible, in fact, that there are propositions of the form "All F are G" and "x is an F" that I believe, where I do NOT believe the corresponding proposition of the form "x is G", simply because I have never gotten around to inferring it. Note carefully that the claim is not that I believe that x is NOT G, just that I fail to believe that it is. In this kind of case, though, you might say that I "implicitly" believe that x is G, meaning something like: If it ever came up, I'd draw the inference and more or less act like I'd believed it all along.

Some people (such as Robert Stalnaker, at least in some moods) would not agree with this. They think the only coherent notion of belief is one according to which I do believe, all along, that x is G. I think those people are nuts, but that is a topic for another day.

The second reason it does not logically follow that John believes that Mushmush should be killed is that John might be irrational. He might just refuse to draw that conclusion, even though he is fully aware of what he believes about green people and of the fact that Mushmush is green. And here we come up against difficult questions about the relation between logic and norms of thought and reason. It's extremely tempting to want to say something like, if John believes all green people should be killed and if John also believes that Mushmush is green, then he ought also to believe that Mushmush should be killed.

But it's unclear whether that is right. Some people (Gilbert Harman is the best-known example) would want to say, no, what John should do is stop believing that all green people should be killed, since, as he himself can see, it leads to the conclusion that his buddy Mushmush should be killed. One response to this is to say something like, well, of course what John ought all things considered to do is stop believing that, but nonetheless, given what he does believe, he ought to believe this other thing, too. That is: As things are, he has sufficient and indeed compelling reason for that other belief, and the fact that his current beliefs give him sufficient reason to believe something he flatly rejects sounds like why he should stop believing what he believes. If so, then perhaps what we should really say is something like: John ought not simultaneously and knowingly (a) to believe that all green people should be killed, (b) to believe that Mushmush is green, and (c) to deny that Mushmush should be killed. The idea is that this trio of attitudes is irrational: Something ought to give.

Obviously, the issues here are exceedingly complex, and I doubt anyone really knows what we should say about this.

This is a nice case of what can go wrong when you (i.e., I) do philosophy too quickly! As Richard charitably suggests, (I think) I was reading the argument (too quickly) to say:

1. John believes that all green people should be killed, and

2. John believes that Mushmush is a green person,

3. Thus, John believes that Mushmush should be killed.

Mitch is right that the original question left "John believes" out of premise 2, so it's clearly not formally valid: 1 could be true, but if John does not believe Mushmush is green (even though he is), then clearly 3 would not follow.

With premise 2 written as here, with "John believes," then it looks much "closer to valid" but "valid" is not like horseshoes or hand grenades, so close does not count. It's hard to see how John could miss the inference, but perhaps he is like some racists in literature who sincerely hold universal derogatory beliefs about another race and sincerely reject that belief about their friend or neighbor who they know is a member of that race (or do they actually reject the universal claim--making an exception for their friend--or do they actually reject that their friend is a member of that race?).

Or maybe, being even more charitable to my former self, I was reading the argument like this:

John believes that: (1) all green people should be killed and (2) Mushmush is a green person, so (3) Mushmush should be killed.

That is, John believes a valid argument. But I think that I doubt that I believed that...